Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the $W$-action on $B$-sheets in positive characteristic
HTML articles powered by AMS MathViewer

by Friedrich Knop and Guido Pezzini
Represent. Theory 19 (2015), 9-23
Published electronically: March 6, 2015


Let $G$ be a connected reductive group defined over an algebraically closed base field of characteristic $p\ge 0$, let $B\subseteq G$ be a Borel subgroup, and let $X$ be a $G$-variety. We denote the (finite) set of closed $B$-invariant irreducible subvarieties of $X$ that are of maximal complexity by $\mathfrak {B}_{0}(X)$. The first named author has shown that for $p=0$ there is a natural action of the Weyl group $W$ on $\mathfrak {B}_{0}(X)$ and conjectured that the same construction yields a $W$-action whenever $p\ne 2$. In the present paper, we prove this conjecture.
  • Armand Borel and Jacques Tits, Homomorphismes “abstraits” de groupes algébriques simples, Ann. of Math. (2) 97 (1973), 499–571 (French). MR 316587, DOI 10.2307/1970833
  • Nicolas Bourbaki, Éléments de mathématiques: groupes et algèbres de Lie, Masson, Paris, 1981 (French). Chapitres 4, 5, et 6.
  • Jonathan Brundan, Dense orbits and double cosets, Algebraic groups and their representations (Cambridge, 1997) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 517, Kluwer Acad. Publ., Dordrecht, 1998, pp. 259–274. MR 1670774
  • Friedrich Knop, On the set of orbits for a Borel subgroup, Comment. Math. Helv. 70 (1995), no. 2, 285–309. MR 1324631, DOI 10.1007/BF02566009
  • George Lusztig and David A. Vogan Jr., Singularities of closures of $K$-orbits on flag manifolds, Invent. Math. 71 (1983), no. 2, 365–379. MR 689649, DOI 10.1007/BF01389103
  • M. Demazure, Séminaire de Géométrie Algébrique du Bois Marie - 1962-64 - Schémas en groupes - (SGA3) - vol. 3, Michel Demazure, Alexandre Grothendieck (Eds.), Lecture notes in mathematics 153, Springer-Verlag, Berlin, New York, 1970.
  • A. A. Premet, Weights of infinitesimally irreducible representations of Chevalley groups over a field of prime characteristic, Mat. Sb. (N.S.) 133(175) (1987), no. 2, 167–183, 271 (Russian); English transl., Math. USSR-Sb. 61 (1988), no. 1, 167–183. MR 905003, DOI 10.1070/SM1988v061n01ABEH003200
  • David I. Stewart, The second cohomology of simple $\textrm {SL}_2$-modules, Proc. Amer. Math. Soc. 138 (2010), no. 2, 427–434. MR 2557160, DOI 10.1090/S0002-9939-09-10088-6
  • È. B. Vinberg, Complexity of actions of reductive groups, Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 1–13, 96 (Russian). MR 831043, DOI 10.1007/BF01077308
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20G15, 14M17, 14L30, 20G05
  • Retrieve articles in all journals with MSC (2010): 20G15, 14M17, 14L30, 20G05
Bibliographic Information
  • Friedrich Knop
  • Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
  • MR Author ID: 103390
  • ORCID: 0000-0002-4908-4060
  • Guido Pezzini
  • Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
  • MR Author ID: 772887
  • Received by editor(s): September 2, 2013
  • Received by editor(s) in revised form: November 10, 2014, and February 3, 2015
  • Published electronically: March 6, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 9-23
  • MSC (2010): Primary 20G15, 14M17, 14L30, 20G05
  • DOI:
  • MathSciNet review: 3318502